A Functional Approach to Vertical Turbulent Transport of Scalars in the Atmospheric Surface Layer

Eddy covariance has been the de facto method of analyzing scalar turbulent transport data. To refine the information available from these data, we derive a simplified version of the turbulent scalar-transport equation for the surface layer, which employs a more explicit form of signal decomposition and dispenses with Reynolds averaging in favour of an averaging operator based on the relevant scalar-flux driving variables. The resulting method, termed functional covariance, provides five areas of improvement in flux estimation: (i) Better representation of surface fluxes through closer correspondence of turbulent exchange with variations in the driving variables. (ii) An approximate 25% reduction in flux uncertainty resulting from improved independence of turbulent-flux samples. (iii) Improved data retention through less onerous quality control (stationarity) testing. (iv) Improved estimation of low-frequency flux contributions through reduced uncertainty and avoidance of driving-variable nonstationarity. (v) Potential elimination of flux-storage estimation when state driving-variables are used to define the functional-covariance flux averaging. We describe the important considerations required for application of functional covariance, apply both functional- and eddy-covariance methods to an example dataset, compare the resulting eddy- and functional-covariance estimates, and demonstrate the aforementioned benefits of functional covariance.